Question

When graphed, the three lines y=-x + 2 y=2x-1, and y= x-2 intersect in such a way that they form a triangle.
What are the coordinates of the three vertices of this triangle?
.
-6
-5
3
1
2 3
4
5 6
7
3
4
-5
-6
OA (2.0), (0, 2), and (-1, -3)
ОВ. (0, 2), (2.0), and (1,-1)
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Answer 1

Answer:

the three vertices are (1, 1), (2, 0), (-1, -3).

Answer 2

The vertices of the triangles are the coordinates of the point of

intersection of the graph of the equation of the three lines.

Correct response:

The coordinates of the three vertices of the triangles are;

E. $\underline{(2, 0), \ (1, -1), \ and \ (-1, -3)}$

How are the coordinates of the vertices obtained?

The equation of the given lines are;

y = -x + 2, y = 2·x - 1, y = x - 2

The point of the intersection of the two lines, gives the vertices, and are

the solution of the two linear equations of the lines.

At the points where the lines intersect, we have;

-x + 2 = 2·x - 1

Which gives;

3·x = 3

x = 1

y = -1 + 2 = -1

A vertex is at the point (1, -1)

The coordinate of the second vertex is given as follows;

2·x - 1 = x - 2

2·x - x = -2 + 1 = -1

x = -1

y = -1 - 2 = -3

The second vertex is; (-1, -3)

The coordinates of the third vertex is given as follows;

-x + 2 = x - 2

2·x = 4

x = 2

y = 2 - 2 = 0

Which gives the point; (2, 0)

• The three vertices are; E. (2, 0), (1, -1), and (-1, -3)

Learn more about linear equations here:

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